23.2.22 problem 7

Internal problem ID [4139]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 7
Date solved : Monday, January 27, 2025 at 08:39:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 19

dsolve((1+x^2)*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = 2 c_{2} x^{2}+c_{1} \sinh \left (2 \,\operatorname {arcsinh}\left (x \right )\right )+c_{2} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 25

DSolve[(1+x^2)*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh (2 \text {arcsinh}(x))+i c_2 \sinh (2 \text {arcsinh}(x)) \]